Question

Can someone please answer this by Friday? A poker deck consists of cards ranked 2; 3;...

Can someone please answer this by Friday?

A poker deck consists of cards ranked 2; 3; 4; 5; 6; 7; 8; 9; 10; J; Q;K;A (13 different ranks), each in four suits, for a total of 52 distinct cards.
(a) What is the probability that a five-card poker hand drawn from a poker deck consists only of cards ranked 8; 9; 10; J; Q;K;A?
(b) Find a probability of Three of a kind. This is, three cards of the same denomination and two cards from two other denominations.

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Answer #1

(a)

Total number of events:

Number of ways of drawing 5 cards from 13 X 4 = 52 cards is given by 52C5 = 2,598,960

Number of favorable vents:

Number of ways of drawing 5 cards from 7 X 4 =28 cards is given by 28C5 = 98,280

So,

the probability that a five-card poker hand drawn from a poker deck consists only of cards ranked 8; 9; 10; J; Q;K;A

= 98,280/ 2,598,960

= 0.0378

So,

Answer is:

0.0378

(b)

Three of a kind has the pattern:

AAABC,

where A,B,C are from different denominations.

The denomination for first 3 cards can be selected in 13C1 = 13 ways.

The suits for the first 3 cards can be selected in 4C3 = 4 ways.

The denominations for last 2 cards can be selected in 12C2 = 66 ways.

The suits for each of the last 2 cards can be selected in 4C1 = 4 ways.

Thus,

probability of Three of a kind =13 X 4 X 66 X 4 X 4/ 2,598,960

= 54912/2,598,960

= 0.0211

So,

Answer is:

0.0211

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